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Q: If you were on the inside of the Sun falling in, the matter closer to the surface doesn’t affect your acceleration, but the matter closer to the core does. Why is that?

Thursday, September 2nd, 2010

The original question was: Plait talks about the “physics of solid bodies” and why, specifically, if you were on the inside of the Sun falling in, the matter “behind” you- closer to the surface- doesn’t affect your acceleration at all, and all that matters is the matter “in front” of you- closer to the core. Why is that?

Physicist: The short, uninteresting answer is that the gravity from any layer above you cancels itself out. If you take any sample layer above you, and you happen to be closer to one side, then you’ll find that the side you’re closer to has more pull on you, but there’s less of it. Conversely, the far side has less pull, but there’s more of it. For a sphere (but not a ring) these forces cancel exactly. So as you fall in you can ignore all the layers above you.

Pick a layer. Anything inside will experience exactly the same amount of pull in every direction, and so, no pull at all.

Answer gravy: One of the greatest tools in the physicist’s tool kit is “Gaussian Surfaces“. They let you shortcut really difficult math problems using pictures and a little reasoning.  Even better, you come across smarter than perhaps you deserve, which is a big plus.

A Gaussian surface is nothing more than an invisible bubble that you draw in space. The “inverse square law” of gravity can actually be rewritten as “the total amount of gravity pointing into the bubble is proportional to the amount of matter inside the bubble”. The arrangement of matter (both inside and outside the bubble) certainly changes how gravity points into (or out) of the bubble, but the total amount of gravity pointing through depends only on the amount of matter inside.

(upper left) when the mass is symmetrical and in the middle, then the gravity is exactly the same everywhere on the surface. (upper right) if the matter is off to the side, then gravity will be stronger, or weaker, or point in different directions at different points on the surface, but the total stays the same. (bottom) matter outside of the Gaussian surface can affect how gravity pokes through, but it can't affect the total.

Now say that your bubble is an exact fit around a sphere of matter. Everything is perfectly symmetric, so there’s no reason for gravity to be any stronger or weaker anywhere and, given the amount of mass inside the sphere, you can figure out how strong the gravity is. Now say you add more matter, but uniformly, on top of your original sphere.

In both situations the total amount of matter inside the bubble is the same, and everything is nice and symmetrical, so the gravity along the surface of the bubble is the same.

The matter inside the sphere has remained the same, so the pull at the surface of that sphere remains the same. As a result, so long as the matter above is at least fairly symmetrical (which is the case for any planet or star you can think of), you can ignore the layers above the surface of the bubble.

Specifically, as you fall farther and farther into the Sun (or Earth, or whatever else is round) you can figure out how much gravity you’re feeling by using a Gaussian surface, for which you only need the matter below you. The layers above will exert no pull on you, and you will exert no net pull on them (for every action/force there is an equal and opposite reaction/force).

This part has nothing to do with the question: You can use Gaussian surfaces to prove some surprising things. Specifically: Dyson spheres work, and black holes have no more gravity than the stars they came from.

From the last argument (above) you know that the layers above you have no net gravitational effect on you. But what if you fall a little way into a planet, and suddenly find that the inside of it is completely hollow? One you’re inside all the layers are layers above you. So there’s no gravity at all inside of a large hollow sphere (at least, none caused by the sphere). If you built a really huge sphere around a star you’d have a “Dyson’s sphere”. The sphere doesn’t pull the star, and the star doesn’t pull the sphere. It’s stable no matter where the star is inside the ball. So long as no one shoves anything, everything will just float neutrally right where it is.

(left) the set up for a Dyson Sphere. The perfectly spherical shell has no gravitational effect on anything inside the sphere, including the star. (center) Miles Dyson, inventor of the Dyson sphere, and future inventor of Skynet. (right) an artist's interpretation of a Dyson sphere.

Now, put a Gaussian surface around a star. There’s a certain amount of matter in the star, and that tells you how much gravity is pointing through the surface. If the star shrinks, who cares? Same amount of mass = same amount of gravity.

The gravity through the outer Gaussian surface stays the same, since both contain the same amount of matter. The gravity through the inner Gaussian surface increases dramatically after the star collapses, because it contains all of the star's mass, instead of just a small part of it.

But if you draw a small Gaussian surface around the core of the star you’ll find that the gravity along the surface is small, because there is (relatively) little mass inside of it. If for some reason you found yourself in the center of the Sun, you’d be floating in zero G’s. Point of fact; you’d also be on fire.

Now when the Star collapses, all of the matter is drawn into a tiny region. Both spheres (see diagram on the right) now contain all of the star’s matter, and thus the same total amount of gravity pokes through them. The only difference is that the inner sphere is smaller, so the gravity has to be more intense to get the same total as the outer sphere.
Black holes do have very intense gravity, but only in the region where the star used to be.

Posted in -- By the Physicist, Astronomy, Math, Physics | No Comments »

Q: Why are orbits elliptical? Why is the Sun in one focus, and what’s in the other?

Wednesday, August 18th, 2010

Physicist: This question always bothered me too.  The short answer is: it falls out of the math.  Specifically, the math of first year physics and second year calculus.  The fact that the Sun is in one focus is just one of those things.  It’s nothing special.  Even less special is the other focus, which contains nothing at all.

Ellipses and their foci have a lot of useful properties. It so happens that an orbiting object traces out an ellipse, with the thing it orbits around at one of the focuses. Coincidence? Yes.

I can’t find a good intuitive reason why orbits are elliptical.  In fact, I can’t even find a mathematical derivation.  So, because it should be found somewhere, I’ll leave the derivation floating in the answer gravy.

Answer gravy: The force of gravity is usually written as ma=F=-\frac{GMm}{R^2}.  You can rewrite this using vector notation as m\ddot{\vec{x}}=-\frac{GMm\vec{x}}{|\vec{x}|^3}, where the dot on top is a time derivative.  To keep the notation both standard and confusing, \vec{x}=(x,y).

\begin{array}{ll}m\ddot{\vec{x}}=-\frac{GMm\vec{x}}{|\vec{x}|^3}\\\Rightarrow\ddot{\vec{x}}=-\frac{GM}{|\vec{x}|^3}\vec{x}\\\Rightarrow\dot{\vec{x}}\cdot\ddot{\vec{x}}=-\frac{GM}{|\vec{x}|^3}\vec{x}\cdot\dot{\vec{x}}\\\Rightarrow\dot{\vec{x}}\cdot\ddot{\vec{x}}=-\frac{GM}{(\vec{x}\cdot\vec{x})^{3/2}}\vec{x}\cdot\dot{\vec{x}}&\left\{\vec{x}\cdot\vec{x}=|\vec{x}|^2\right.\\\Rightarrow\frac{d}{dt}\left[\frac{1}{2} \dot{\vec{x}}\cdot\dot{\vec{x}}\right]=\frac{d}{dt} \left[\frac{GM}{(\vec{x}\cdot\vec{x})^{1/2}} \right]&\left\{\frac{d}{dt}\left(\vec{x}\cdot\vec{x}\right)=2\vec{x}\cdot\dot{\vec{x}}\right.\\\Rightarrow \frac{d}{dt}\left[|\dot{\vec{x}}|^2 \right]=\frac{d}{dt}\left[\frac{2GM}{|\vec{x}|}\right]\\\Rightarrow |\dot{\vec{x}}|^2=\frac{2GM}{|\vec{x}|}+c\end{array}

c is an “integration constant“, it can be any number.  Jumping over to polar coordinates \left(\begin{array}{l}x=R\cos{(\theta)}\\y=R\sin{(\theta)}\end{array}\right) you can rewrite the usual velocity in terms of how fast you’re moving toward or away from the Sun (\dot{R}) and how fast you’re going around (\dot{\theta}).

\begin{array}{ll}\Rightarrow\dot{R}^2+R^2\dot{\theta}^2=\frac{2GM}{R}+c&\left\{\begin{array}{ll}|\vec{x}|=R\\|\dot{\vec{x}}|^2=\dot{R}^2+R^2\dot{\theta}^2\end{array}\right.\\\Rightarrow\left(\frac{dR}{d\theta}\dot{\theta} \right)^2+R^2\dot{\theta}^2=\frac{2GM}{R}+c&\left\{\frac{dR}{dt}=\frac{dR}{d\theta}\frac{d\theta}{dt}\right.\\\Rightarrow\left(\left(\frac{dR}{d\theta}\right)^2+R^2\right)\dot{\theta}^2=\frac{2GM}{R}+c\\\Rightarrow\left(\left(\frac{dR}{d\theta}\right)^2+R^2\right)\frac{L^2}{R^4}=\frac{2GM}{R}+c&\left\{R^2\dot{\theta}=L\right.\\\Rightarrow\left(\frac{1}{R^2}\frac{dR}{d\theta}\right)^2+\frac{1}{R^2}=\frac{2GM}{L^2R}+\frac{c}{L^2}\\\Rightarrow\left(\frac{1}{R^2}\frac{dR}{d\theta}\right)^2+\frac{1}{R^2}=2\alpha\frac{1}{R} +C&\left\{\begin{array}{l}C=\frac{c}{L^2}\\\alpha=\frac{GM}{L^2}\end{array}\right.\end{array}

L is the angular momentum of the planet in question, and it’s constant.  It may seem silly but, with the advantage of foresight, it’s better to solve this problem in terms of 1/R instead of R.

\begin{array}{ll}\Rightarrow \left(-\frac{dS}{d\theta}\right)^2+S^2=2\alpha S +C&\left\{\begin{array}{l}S=\frac{1}{R}\\\frac{dS}{d\theta}=-\frac{1}{R^2}\frac{dR}{d\theta}\end{array}\right.\\\Rightarrow-\frac{dS}{d\theta}=\sqrt{-S^2+2\alpha S+C}\\\Rightarrow d\theta=\frac{-dS}{\sqrt{-S^2+2\alpha S+C}}\\\Rightarrow\int d\theta=-\int\frac{dS}{\sqrt{-S^2+2\alpha S+C}}\\\Rightarrow\theta+D=-\int\frac{dS}{\sqrt{C+\alpha^2-(S-\alpha)^2}}\\=\int\frac{\sqrt{C+\alpha^2}\sin{(u)}du}{\sqrt{C+\alpha^2-(C+\alpha^2)\cos^2{(u)}}}&\left\{\begin{array}{l}S-\alpha=\sqrt{C+\alpha^2}\cos{(u)}\\dS=-\sqrt{C+\alpha^2}\sin{(u)}du\end{array}\right.\\=\int\frac{\sin{(u)}du}{\sqrt{1-\cos^2{(u)}}}\\=\int\frac{\sin{(u)}du}{\sqrt{\sin^2{(u)}}}\\=\int du\\\Rightarrow\theta+D=u\\\Rightarrow\cos{(\theta+D)}=\cos{(u)}\\\Rightarrow\sqrt{C+\alpha^2}\cos{(\theta+D)}=\sqrt{C+\alpha^2}\cos{(u)}\\\Rightarrow\sqrt{C+\alpha^2}\cos{(\theta+D)}=S-\alpha\\\Rightarrow\frac{1}{R}=S=\alpha+\sqrt{C+\alpha^2}\cos{(\theta+D)}\\\Rightarrow R=\frac{1}{\alpha+\sqrt{C+\alpha^2}\cos{(\theta+D)}}\\\Rightarrow R=\frac{P}{1+\epsilon\cos{(\theta+D)}}&\left\{\begin{array}{l}P=\frac{1}{\alpha}=\frac{L^2}{GM}\\\epsilon=\sqrt{\frac{C}{\alpha^2}+1}\end{array}\right.\end{array}

The choice of P and ε may seem arbitrary (and it is), but it has some historical relevance.  P is called the “semi-latus recturn” and it basically describes the size of the orbit.  ε is called the “eccentricity”, and it describes how lopsided the orbit is.  ε=0 means the orbit is a circle, 0<ε<1 means the orbit is elliptical, and 1≤ε means that the orbit is open (not actually orbiting).  For reference, the Earth’s eccentricity is ε=0.01671123 and Halley’s comet’s is ε=0.967.

D just describes what direction the far side of the ellipse points in, so it’s not actually important to the overall shape.

It turns out that this last equation relating R and θ is all you need to define an ellipse, such that the center of the system, (0,0), is at one of the foci.  Here’s a proof:

An ellipse with a focus at (0,0) can be written \frac{(x+F)^2}{A^2}+\frac{y^2}{B^2}=1 where F is the distance from the center of the ellipse to the focus and F^2=A^2-B^2.

\begin{array}{ll}R=\frac{P}{1+\epsilon\cos{(\theta)}}\\\Rightarrow R+\epsilon R\cos{(\theta)}=P\\\Rightarrow \sqrt{x^2+y^2}+\epsilon x=P\quad\quad\quad\left\{\begin{array}{l}x=R\cos{(\theta)}\\y=R\sin{(\theta)}\end{array}\right.\\\Rightarrow \sqrt{x^2+y^2}=P-\epsilon x\\\Rightarrow x^2+y^2=P^2-2P\epsilon x+\epsilon^2x^2\\\Rightarrow (1-\epsilon^2)x^2+2P\epsilon x+y^2=P^2\\\Rightarrow x^2+2\frac{P\epsilon}{1-\epsilon^2} x+\frac{y^2}{1-\epsilon^2}=\frac{P^2}{1-\epsilon^2}\\\Rightarrow x^2+2\frac{P\epsilon}{1-\epsilon^2} x+\left(\frac{P\epsilon}{1-\epsilon^2}\right)^2+\frac{y^2}{1-\epsilon^2}=\frac{P^2}{1-\epsilon^2}+\left(\frac{P\epsilon}{1-\epsilon^2}\right)^2\\\Rightarrow \left(x+\frac{P\epsilon}{1-\epsilon^2}\right)^2+\frac{y^2}{1-\epsilon^2}=\frac{P^2(1-\epsilon^2)}{(1-\epsilon^2)^2}+\frac{P^2\epsilon^2}{(1-\epsilon^2)^2}\\\Rightarrow \left(x+\frac{P\epsilon}{1-\epsilon^2}\right)^2+\frac{y^2}{1-\epsilon^2}=\frac{P^2}{(1-\epsilon^2)^2}\\\Rightarrow \frac{\left(x+\frac{P\epsilon}{1-\epsilon^2}\right)^2}{\left(\frac{P^2}{(1-\epsilon^2)^2}\right)}+\frac{y^2}{\left(\frac{P^2}{1-\epsilon^2}\right)}=1\end{array}

Put it all together, and you’ll find that this is definitely an ellipse with a focus at the point (0,0), the location being orbited around (like the Sun for instance).

Posted in -- By the Physicist, Astronomy, Physics | 2 Comments »

Q: Is it possible to fill a black hole? If you were to continuously throw galaxies worth of matter into a black hole, would it ever fill up? And what would theoretically happen if all the matter in the universe was thrown into a single black hole?

Wednesday, May 26th, 2010

Physicist: Nope.

A blackhole is already the result of over filling. A blackhole is to mass as the rage virus is to people; throwing more at it just makes it more dangerous. However, unlike zombies, blackholes do eat each other.

The more matter that falls into a blackhole, the bigger the blackhole becomes. For example; the blackhole at the center of our galaxy (Sagittarius A*) has a mass of about 4 million suns, which is already the size of some small galaxies. Small globular clusters anyway.

If all the matter in the universe were chucked into the same giant blackhole you’d have: a really giant blackhole.

Posted in -- By the Physicist, Astronomy, Physics | 2 Comments »

Q: Spectroscopy?

Sunday, May 23rd, 2010

The complete question was: What is spectrum? What spectrum does the absolute black body have? Why do different bodies have different spectra? What is spectroscopy and how is it used in science? Why do different elements in star spectrum have different frequencies or what?

Physicist: If you have a sample of light, from a star, or some kind of lamp, or whatever, then its spectrum describes how much of each frequency of light shows up in that sample.  For example, a laser has a very “sharp” spectrum (all concentrated at one frequency), while sunlight has a very “broad” spectrum (many frequencies).  “Spectroscopy” is the science of gleaning information about something by looking at the spectrum of light it emits, or even absorbs.

The spectrum of a perfectly black body is, not surprisingly, called the “black body spectrum”.  The the intensity (I) of light at a given frequency (\nu) in the black body spectrum is given by I=\left(\frac{2h\nu^{3}}{c^2}\right)\frac{1}{e^{\frac{h\nu}{kT}}-1}, where h, c, and k are Planck’s constant, the speed of light, and Boltzmann’s constant respectively.

What’s amazing about this formula is that the only variable is temperature (T).  So the spectrum of a perfectly black object is determined entirely by its temperature.  The black body spectrum is also a very good approximation for the spectrum emitted by pretty much any thermal source.  Such as light bulbs, hot irons, fires, people, stars, etc.  In this case light is emitted by atoms slamming into each other and losing energy as light “splashes” off (smacking atoms jiggles their electrons, and jiggling charges is what makes light).

The peak of the black body spectrum moves to higher frequencies as temperature increases. Albireo, a binary star system, is a dramatic example of two different temperatures being indicated by two different colors.

By looking at the spectrum of a light source you can (often) tell what the source of that light is made of, what its temperature is, and even what the light has passed through before it gets to you.  The electrons in atoms can only exist in certain, discrete energy levels.  As such, the light that they can emit or absorb corresponds exactly to the amount of energy that can be gained or lost by jumping between energy levels.  The set of light frequencies that a particular element emits is called that element’s “atomic spectra“.

Left: the spectra of Argon, Helium, Hydrogen, and Mercury. Right: by passing the light through a difraction grating or prism you can tell what kind of gas is in it.

Different atoms have different spectra because the higher the atomic number, the higher the number of protons in the nucleus, and the greater the pull on the electrons.  The electrons in turn stack up and have bizarre magnetic interactions.  The interaction between electrons in an atom are very non-linear, and really complicated.  So adding one new electron will change the spectrum completely.  In fact, beyond hydrogen, the atomic spectra can’t be accurately calculated without a good computer.

Elements also have an “absorption spectra”, that corresponds exactly with emission spectra.  For example, big chunks of the infrared light frequencies are in the absorption spectrum of CO2.  Hence the famous green house effect.

The spectrum of sunlight, as veiwed from space (the veiw is clear from there). Rather than make one long rainbow, this was looped (like text on a page) to save room. The gaps in the spectrum tell us what gases are present in the outer layers of the sun.

Because each element (and molecule) has it’s own spectrum, we can look at a light source and see immediately which chemicals are present.  And by measuring (very carefully) how intense each line is we can tell how much of each chemical is present.

Even slicker, the atomic spectrum of each element is the same everywhere in the universe.  So if we look at a star and its hydrogen lines (which tend to be the clearest and most dominant) are all shifted to lower frequencies, then we know that that star must be moving away from us.  This is caused by the Doppler effect, and is called “redshift” because the lines look redder.

Spectroscopy is in use here on Earth to quickly determine what substances, and how much, can be found in a sample.  Generally by shining light (of a well known spectrum) through it.  For example, you can quickly check ozone levels, humidity, and even the size of particulate pollution, from space by watching sunlight filter through the atmosphere.  There are better methods (chemical based measurements) so spectrographic techniques are not en vogue, but they can be used in a pinch.

Also, radar guns and infra red thermometers are basically spectrometers with a single, specific function.

But the science of spectroscopy is mostly at home in astronomy circles, since they have literally nothing else to work with.  Zoologist can smell what they study, electrical engineers can be shocked.  But astronomers have to stare at the sky really hard, and measure spectra.  Even the discovery of planets around other stars comes down to measuring the red-shifting and blue-shifting of the parent star as its planets make it wobble.  We know what interstellar gas and dust clouds are made of by looking at star light filtering through them, and measuring the absorption spectra.

Really, everything we know about stuff outside of the solar system (everything beyond “look, stars!”) is based on spectroscopy.

Posted in -- By the Physicist, Astronomy, Physics, Quantum Theory | 1 Comment »

Q: Is it possible to breach the center of a nebula?

Wednesday, May 19th, 2010

The original question was: Is it possible to breach the center of a nebula? All the gases around it would make it hard for us to achieve this correct?

Physicist: It wouldn’t be too bad.  If you were in a nebula, you probably wouldn’t notice the gas at all.  The difference between deep space and the inside of a nebula is pretty small.  The fact that we can even see nebulae at all is due to the fact that when we look at them, we’re looking through several light years of dust and gas, which adds up.  If you were actually there, by the time the gas was dense enough that you’d notice it at all, it would already be in the process of collapsing and you’d find yourself inside a new star in short order.

The Orion Nebula. Unlike most space pictures, this is really what you'll see even with a backyard telescope. This object is about 24 light years across (gargantuan). Those bright blue stars are the result of the gas getting a little too dense and collapsing.

Nebulae are in general huge.  So getting to the middle of one in any reasonable amount of time would involve moving at relativistic velocities (near light speed).  For example, the Orion Nebula is about 24 light years across.  To get from the edge to the center in less than several years would require moving at around 95% of light speed or faster.  But at speeds like that even small pieces of grit (common in planetary nebulae especially) become very dangerous.

So, yes, you can definitely get to the middle of a nebula.  But you either need to take your time, or have a fast, well armored ship.

Posted in -- By the Physicist, Astronomy | No Comments »

Q: How/when will the world end?

Monday, April 26th, 2010

Physicist: To answer this question definitively would require the destruction of at least a couple dozen other worlds.  But failing that, guesswork:

The little things (people): In the short term (less than several million years) the biggest threat the Earth faces is people.  We’ve already got the Holocene mass extinction going for us, now we’ve just got to step up our game and go for broke.  Hey, Coalition of the Willing!  I think I saw North Korea stealing your cup cakes.  Also, it’s too cold in the winter.  Couldn’t we burn a teraton of coal or something?

Boring, Regular Extinction: It we (Homo sapiens) follow the same fate as all of our predecessors and cousins (homo habilis, rudolfensis, georgicus, ergaster, erectus, cepranensis, antecessor, heidelbergensis, rhodesiensis, and neanderthalensis, for example), then it’s very likely that we’ll be extinct within the next 100,000 to 1,000,000 years.  Statistically speaking anyway.

Total carbon re uptake: Over very large time scales the sun is getting brighter (along the lines of about 10% per billion years).  Astrophysicist Brownlee and paleontologist Peter Ward have written a book espousing the idea that this gradual brightening will cause the Earth to heat up and the natural chemical processes that absorb CO2 from the air (and lock it away in sediment) will speed up.

"Main sequence stars", which include the sun, are surprisingly stable for a very long time. They do change a little, increasing their brightness by about 10% every billion years.

They figure that inside of 500 million years there won’t be enough CO2 in the atmosphere to support plant life, and that would be the end of complex life.  Although life has been around for at least 3.5 billion years, the interesting stuff (animals) have only been around for about 500 million years.  So if Brownlee and Ward are right, we’re only about halfway done (not nearing the end).

It may seem strange to talk about the loss of CO2 being the end of the world when we so often talk about the dangers of too much CO2.  The difference is in the time scales.  The spike of CO2 we worry about today is on the scale of centuries, while the long term absorption of CO2 is on a time scale a million times larger (unnoticeable in the short term).

Dynamo shutdown: The Earth’s magnetic field is the result of iron rich (electrically conductive) stuff flowing around in the Earth’s core.  The currents are driven by radioactive heating which causes convection, specifically the decay of radioactive potassium, uranium, and thorium.  The half-lives of these materials are 1.25 billion, 4.5 billion, and 14 billion years respectively, so most of the original fuel has already been used up.

The exact nature of magnetic dynamos is not terribly well known, and is still an active area or research.  We don’t know for certain what the minimum energy input is needed to keep the damn thing running.  We do know that it’s certainly possible for a planetary magnetic dynamo to shut down (Mars’ shut down at least a couple billion years ago).  If our dynamo shuts down, then our magnetic field will vanish and (in fairly short order) the atmosphere will be stripped away by solar wind, as happened on Mars.

Never-ending Summer: The increase in the Sun’s output will make it too hot for liquid water on Earth in about 1 billion years.  With the oceans boiled away the pressure everywhere on Earth will be about the same as the pressure on the ocean floor.  The difference between Venus and Earth will be academic.  No matter what else happens before then, this will be the end of life on Earth.

SPF 5,000,000,000,000,000: Somewhere around 5 to 7 billion years from now the Sun will start to run out of fuel.  Ironically this will actually make the core hotter as it collapses in on itself.  The top layers will fluff up and (probably) envelope all the inner planets, including Earth.  For obvious reasons this is called the “red giant” phase of the Sun’s life.  The solar system will eventually settle down with the gas giants still in place, the inner solar system missing, a white dwarf star where the Sun used to be, and the trans-neptunian stuff completely unaffected.

The Sun as we see it today (yellow), and the Sun in its fluffier red giant phase (red).

Lights out: If by “end of the world” you mean “end of the universe”, then a good end of everything is the end of the age of stars.  The universe started out made up of about 75% hydrogen, but today is only about 70% hydrogen.  Stars are almost completely powered by hydrogen fusion, so assuming that the consumption of the universe’s hydrogen is stays constant (which isn’t a particularly good assumption), then there will be almost no stars left in 250 to 300 billion years.

The big rip: Not only is the universe expanding, but the speed of that expansion is increasing.  The expansion is a little hard to picture because the expansion isn’t about things moving away from each other in space, it about the space in between things actually expanding.  Right now the effect is small enough that it can only be seen on huge, inter-galactic, scales.  But eventually the expansion with be so rapid that the space between the planets and their stars will increase so fast that the planets will be pulled into open space, and not long after than (as in a couple of months or so) the space between atoms will increase so fast that everything will be completely torn apart and atomized.  This is called the “big rip”.  Some estimates put the big rip about 20 billion years out, and some say it won’t happen at all.

Posted in -- By the Physicist, Astronomy, Biology, Paranoia, Physics | 1 Comment »

Video: The Scientific Investigation of Aliens – Evidence Examined

Wednesday, April 14th, 2010
This talk given at Nerd Nite (NYC) by the Mathematician discusses some of the evidence that has been proposed for the idea that technologically advanced aliens have already arrived on earth, including UFO photographs, crop circles, and abduction stories.

The PowerPoint presentation of this lecture, including references:

Download the Scientific Investigation of Aliens PowerPoint Presentation

Part 1 of the video of this lecture:

Part 2 of the video of this lecture:

References:

Polls

Roper Poll Survey 1999 :

http://www.ufoevidence.org/documents/doc850.htm

Public Opinion Polls on UFOs :

http://www.ufoevidence.org/topics/PublicOpinionPolls.htm

CNN/TIME Poll 1997 :

http://www.cnn.com/US/9706/15/ufo.poll/

Gallup Poll 2005:

http://www.gallup.com/poll/19558/Paranormal-Beliefs-Come-SuperNaturally-Some.aspx

Hallucination Poll Data :

“Prevalence of hallucinations and their pathological associations in the general population”, 2000 by Maurice M. Ohayon

Crop Circles

The International Crop Circle Database :

http://ccdb.cropcircleresearch.com/index.cgi

Why Crop Circles Can’t Be Hoaxed :

http://theconversation.org/booklet2.html

Abductions

Hill Abduction:

http://en.wikipedia.org/wiki/Betty_and_Barney_Hill_abduction

Kenneth Arnold UFO Sighting:

http://en.wikipedia.org/wiki/Kenneth_Arnold_unidentified_flying_object_sighting

Susan Blackmore on Aliens :

http://www.susanblackmore.co.uk/journalism/ns94.html

John Edward Mack :

http://en.wikipedia.org/wiki/John_Edward_Mack

Astronomy

Number of Planets in the Galaxy :

http://en.wikipedia.org/wiki/Extraterrestrial_life

Number of Galaxies in the Universe :

http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/021127a.html

Number of planets in our galaxy :

http://www.madsci.org/posts/archives/2000-01/948204035.As.r.html

Meteorites :

http://en.wikipedia.org/wiki/Meteorite#Fall_phenomena

Other Info

Photo Tampering Throughout History :

http://www.cs.dartmouth.edu/farid/research/digitaltampering/

Alien Abduction Insurance:

http://en.wikipedia.org/wiki/Alien_abduction_insurance

Alien Abduction Insurance Articles :

http://www.alienabductioninsurance.com/articles.html

Aliens and Children :

http://www.aliensandchildren.org/

Developments in Crop Circles Over Time :

http://www.cropcircles.net/

Top 10 Controversial pieces of evidence for extraterrestrial life :

http://www.newscientist.com/article/dn9943-top-10-controversial-pieces-of-evidence-for-extraterrestrial-life.html

The Drake Equation :

http://en.wikipedia.org/wiki/Drake_equation

The Flake Equation :

http://xkcd.com/718/

UFOs :

http://en.wikipedia.org/wiki/UFO

Causes of Hallucinations :

http://www.wrongdiagnosis.com/h/hallucination/causes.htm#causeslist

Crop Circle :

http://en.wikipedia.org/wiki/Crop_circle

Sleep Paralysis :

http://en.wikipedia.org/wiki/Sleep_paralysis

Water Bears :

http://en.wikipedia.org/wiki/Water_bear

Videos

Best of UFOs (part 1) :

http://www.youtube.com/watch?v=6XXOvUwr2YU

Documentaries About Aleins :

http://www.hyper.net/ufo/video-documentaries.html

Crop Circle Being Made (Schofields Quest – Doug Bower 1994) :

http://www.youtube.com/watch?v=XkGbnUXfh4U

UFO sighting (part 2/3) :

http://www.youtube.com/watch?v=-iVYCYjso-U&feature=player_embedded

National Geographic Crop Circles :

http://video.nationalgeographic.com/video/player/science/weird-science-sci/uk_cropcircles.html

Why people believe strange things:

http://www.ted.com/talks/michael_shermer_on_believing_strange_things.html

Photos

Best UFO Photos:

http://www.ufocasebook.com/bestufopictures.html

Strange Flying Machines Slideshow :

http://www.slideshare.net/webtel125/strange-flying-machines-presentation-793157

UFO Photo Competitions :

http://fx.worth1000.com/contests/8300/sightings-7

Circle Makers :

http://www.circlemakers.org/totc2007.html

UFO Drawings :

http://www.ufo-blog.com/ufo-blog/2010/02/sketches-from-fifth-tranche-of-mod-ufo.html

Three spooky UFO vidoes :

http://www.youtube.com/watch?v=7WYRyuL4Z5I

UFO Haiti :

http://www.youtube.com/watch?v=up5jmbSjWkw

List of Military Aircraft in the United States :

http://en.wikipedia.org/wiki/List_of_military_aircraft_of_the_United_States

Balloon Boy Balloon :

http://s2.hubimg.com/u/1922877_f520.jpg

Sun Dogs:

http://en.wikipedia.org/wiki/Sun_dogs

Lenticular Clouds :

http://en.wikipedia.org/wiki/Lenticular_cloud

Photoshopped Images :

http://www.funnydb.com/Pictures/Celebrities/mona_diesel-3320.html

Books

The Demon Haunted World by Carl Sagan :

http://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469


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Posted in -- By the Mathematician, Astronomy, Skepticism, Videos | No Comments »

Q: Are there physical limits in the universe other than the speed of light?

Wednesday, March 10th, 2010

Physicist: Hells yeah.

Fastest fast: This is worth commenting on since you often hear “nothing can travel faster then light”, but the justification is almost always missing.  The universe seems to be pretty happy thinking of the speed of light as being the same to everybody first (Maxwell’s Laws give you the speed of light, but Maxwell’s laws are the same to everybody so the speed of light is the same to everybody), and as a speed limit second.  Since you always see light moving at the same speed, then no matter how much you speed up, it will always pass you by.  So catching up to it isn’t an option, and everyone will always see you traveling slower than the speed of light.

Densest dense: The harder you compress something, the denser it becomes.  Normally this is reflected in the distance between atoms shrinking.  However, if the pressure is great enough, the atoms will find that it’s easier to have their electrons merge with their protons which then turn into neutrons (and also spit out neutrinos, but whatever).  Without battling electron shells, the once mostly-empty atoms can be packed nucleus-to-nucleus.  Pressures and densities this high only seem to show up in neutron stars (guess where the name comes from).  By way of comparison, here are some densities (in kilograms per liter): Air = 0.0012, People = 1, the Sun = 1.4, Iron = 7.8, Gold = 19.3, Neutron Star = 500,000,000,000,000.

You can also cheat a little.  If a neutron star has a mass of more than about 5 Suns it will collapse into a blackhole, which is technically more dense.

Coldest cold: You might have guessed: zero.  Specifically 0°K = -273°C = -460°F.  However, this is more of an “asymptotic limit” and can never quite be reached.  An object with a temperature of absolute zero will have no atomic movement (heat) whatsoever, but that’s not possible.  One way of thinking about it is in terms of the Heisenberg uncertainty principle which, in a paraphrased nutshell, states: “You can’t have both a perfectly certain position and a perfectly certain momentum”.  Where \Delta x and \Delta p are the position and momentum errors respectively, the uncertainty principle can be written: \Delta x \Delta p \ge \frac{\hbar}{2}.

So if you’ve got a substance and you have any idea where it is (\Delta x < \infty), then you can’t be sure that the momentum is zero, and the object will always have at least a little atomic movement.  Most people who have heard of Heisenberg’s uncertainty principle are under the impression that it’s a limit on how well we can know about an object.  In fact, it’s far better to think of it as a description of how well the universe can know about an object.

Despite the difficulties imposed by the uncertainty principle, we can still get things crazy cold.  The world record for lowest temperature now stands at 0.0000000001°K = 0.1 nK.

Hottest hot: There are actually two limits here, depending on how you phrase the question.  The first is the theoretical upper limit, which depends on which theory you’re working with, but is often quoted around 1030 °K.  These limits have to do with “the graininess” of space, and how much energy can be forced into a particular region.

The second kind of limit is more practical.  As a gas is heated its atoms move faster and faster.  When they collide they bounce of each other and often create photons (light), which generally just go on to push other atoms around.  However, as the temperature approaches about 4 billion °C, the atoms of the gas will often have enough energy to create electron/positron pairs (“E=mc2“, where “E” is the kinetic energy of the gas atoms, and “m” is the total mass of the electron/positron pair).  Normally these newly created particles will almost immediately find other electrons and positrons and annihilate, creating light.  But sometimes they’ll create neutrinos instead of light.  Neutrinos are “weakly interacting” (which is science speak for “goes through walls, no problem”), so the energy used to create them just flies into space, never to be seen again (or just about never).  This has the effect that a gas with a temperature above around 4,000,000,000°C will cool off on its own (without seeming to radiate any energy).  For comparison, the core temperature of the Sun is about 15.7 million °C.

The Sudbury neutrino detector: 40 feet across, and among the more evil looking things ever built. Image stolen without remorse from "http://zuserver2.star.ucl.ac.uk/~idh/apod/ap990623.html"

This is sometimes important during stellar collapse.  If a star needs to have a core temperature above the cut-off point to hold itself up, then it’s not going to hold itself up.

Smallest small: Again, for “uncertainty principle type reasons” it doesn’t make sense to talk about objects or events smaller than the Planck scale, which is about 10-35m.  So far, nobody can think of anything in the universe, at any scale, that would really care, or be able to tell the difference between two points separated by 10-35m.

Emptiest empty: One version of the Heisenberg uncertainty principle can be written “\Delta E \Delta t \ge \frac{\hbar}{2}“, which means that the time and energy of something can’t both be perfectly well known (not even by the universe, the quantities themselves are uncertain).  If you apply this principle to empty space you’ll notice that over short enough time scales there will be measurable, non-zero energy, and over really short time scales you’ll find particles popping in and out of existence.  These particles are called “virtual particles”, and this phenomena is sometimes described as a “particle foam”.

So even with a perfect vacuum, you’ll still have crap around.  This crap is often called the “vacuum energy” or “zero point energy”.

One of the few examples of a device that can harness the vacuum energy of the universe to charge your chrystals or whatever. This illustration of "pyramid power" stolen from "http://www.merlinsrealm.com/pyramid-power.htm"

Sadly, harvesting the vacuum energy is physically impossible (it would violate the uncertainty principle).  The vacuum energy amounts to about 10-13J/m3, or about “the energy a baseball has falling off a table per volume of Lake Superior“.

Posted in -- By the Physicist, Astronomy, Physics, Quantum Theory, Relativity | 3 Comments »

Q: A flurry of blackhole questions!

Thursday, February 18th, 2010

Q: How much of the universe’s mass is currently in black holes?

Blackholes fall into two basic categories: stellar mass blackholes which have a mass of 3 to 30 Suns (give or take), and super-massive blackholes which usually have masses of more than 100,000 Suns.  Even in our own galaxy it’s essentially impossible to determine whether or not stellar mass blackholes are present.  I mean… they’re black, and they’re not heavy enough to throw around the nearby stars.  However, the supermassive blackholes do throw nearby stars around.  And that star-chucking property has allowed us to find that they have a mass of roughly 0.1% of the “bulge-mass” of the galaxies they sit in (the bulge is just the part of a galaxy that isn’t a disk).  So if I had to make a flying guestimate, I’d say that somewhere around 0.2% of the mass of any given galaxy is tied up in blackholes.

Q: Is there a graph of the number of black holes created since the big bang?

Probably.  Blackholes form from large stars, and large stars tend to have short lifetimes (a mere several million years).  So there should be a pretty sharp correlation between star formation rates and blackhole formation rates.  However, star formation rates are also notoriously difficult to measure.

Q: When was the first black hole created and when will the last one be?

“Primordial Blackholes“, if they exist, would have formed almost instantly after the big bang.  If the Big Rip happens, then you can expect the last blackholes to form 50 million years before the end of the universe (give or take).  Otherwise, there’s no telling.

Q: How old will the universe be when black holes start to evaporate, if they even do?

Primordial blackholes should be popping right now.  The lightest stellar-mass blackholes (3 suns) won’t start evaporating until after the universe has cooled to below their Hawking temperature, which should be in about 13 billion years, when the universe is twice as old.  However, one age-of-the-universe is chump change compared to the 1069 years (about 10 billion trillion trillion trillion trillion times the age of the universe) it will take for the first stellar-mass blackholes to completely evaporate.

Q: Could all black holes evaporate away in a expanding cooling  universe?

Yup.

Q: What happens to the universe if all the back holes evaporate away?

No more blackholes?

Posted in -- By the Physicist, Astronomy, Physics | 1 Comment »

Q: Is the universe infinitely old?

Thursday, February 11th, 2010

Physicist: Normally this question is only used to start fights.

Some theories posit that the big bang was the beginning of everything, and that it doesn’t make sense to talk about anything earlier, while others say that it may be impossible for the universe to have a beginning or end.  Both options are terrible.

We can track the progress of the universe all the way back to only moments after the big bang, but no further.  So we’ll never actually be able to see what happened at the instant of the big bang.  However, there are some pretty slick tools that allow us to extract results by studying the crap out of how spacetime behaves today.  Notably the Hawking Singularity Theorem.  We may be able to determine if the the big bang was a singularity (with nothing before), or just a severe “pinching” of the universe (with stuff happening before).

You can picture this as something like trying to figure out whether or not your sheets are pinned together in one place based on how they’re folded and bunched up in another place.  It’s tricky.

Bed sheets: More complicated than spacetime.

However, for all practical purposes the universe is about 15 billion years old (give or take).  If there was anything around before then, it got messed up good by the big bang.

Posted in -- By the Physicist, Astronomy, Physics | No Comments »

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